Finite Group Databasebeta

← #13127981

Subgroups — #13127981

Order 1664.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719474C211yesmaximal, characteristic, complemented
2#11719471C211yesmaximal, characteristic, complemented
3C13×#510C211yesmaximal, characteristic, complemented
4#11718855C211yesmaximal, characteristic, complemented
5C2×#88068C211yesmaximal, characteristic, complemented
6#11718580C212yesmaximal, complemented
7#11718579C212yesmaximal, complemented
8#11718575C212yesmaximal, complemented
9D13×SD32C212yesmaximal, complemented
10#11718569C211yesmaximal, characteristic, complemented
11#11718568C211yesmaximal, characteristic, complemented
12#88256—21no—
13#88254—21no—
14C13×#135C2211yescharacteristic
15C2×C13×Q16C2211yescharacteristic, complemented
16#88203—21no—
17#88196—21no—
18#88173C2212yes—
19#88173C2212yescomplemented
20#88172—22no—
21Q16×D13C2212yescomplemented
22#88168—22no—
23D8×D13C2212yes—
24#88158C2211yescharacteristic, complemented
25C2×D104C2211yescharacteristic
26#88155C2211yescharacteristic
27C13×Q32C2212yescomplemented
28C13×SD32C2212yescomplemented
29C13×M32C2211yescharacteristic, complemented
30#88069C2211yescharacteristic, complemented
31#88068C2212yescomplemented
32#88068C2212yescomplemented
33#88068C2211yescharacteristic, complemented
34#88067C2211yescharacteristic, complemented
35#88066C2211yescharacteristic, complemented
36C2×#6090C2211yescharacteristic, complemented
37#88040C2212yescomplemented
38D208C2212yescomplemented
39#88038C2212yescomplemented
40C16×D13C2212yescomplemented
41C13×#41—21no—
42C2×Q8×C13—21no—
43#6131—22no—
44#6131—22no—
45#6131—41no—
46Q8×D13—22no—
47Q8×D13—41no—
48D4×D13—22no—
49D4×D13—42no—
50#6127—21no—
51#6127—42no—
52#6127—41no—
53#6127D411yescharacteristic
54C2×D52—21no—
55C2×D52—41no—
56C13×Q16—21no—
57C13×Q16C2312yes—
58C13×Q16C2311yescharacteristic
59C13×SD16—21no—
60C13×D8C2311yescharacteristic
61C2×C8×C13C2311yescharacteristic
62#6107—22no—
63#6106—22no—
64#6106—22no—
65#6104—22no—
66#6099D411yescharacteristic
67Dic52C2311yescharacteristic
68D104—21no—
69D104C2311yescharacteristic
70D104C2312yes—
71#6095—21no—
72#6094D412yes—
73C8×D13C2312yes—
74C13×C16C2312yes—
75#6090C2311yescharacteristic
76#6090C2311yescharacteristic
77#3416—131nomaximal, Sylow
78C22×D13—41no—
79C22×D13—42no—
80Q8×C13—21no—
81Q8×C13—22no—
82Q8×C13—41no—
83D4×C13—21no—
84D4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13C2×D411yescharacteristic
88C22⋊D13—41no—
89C22⋊D13—42no—
90C22⋊D13D812yes—
91D52—21no—
92D52—22no—
93D52—42no—
94D52—42no—
95D52—41no—
96D52D811yescharacteristic
97C4×D13—42no—
98C4×D13—41no—
99C4×D13—42no—
100C4×D13—42no—
101C4×D13C2×D412yes—
102Dic26—21no—
103Dic26—42no—
104Dic26D811yescharacteristic
105C8×C13C2×D411yescharacteristic
106C8×C13C2411yescharacteristic
107#1055C2×D412yes—
108#578—131no—
109#576—131no—
110#510—132no—
111#510D1311yescharacteristic, complemented
112#509—132no—
113#509—131no—
114#508—131no—
115#508—132no—
116C2×SD32—131no—
117C2×SD32—132no—
118#504—131no—
119C22×C13—41no—
120C22×C13C2×D811yescharacteristic
121C2×D13—41no—
122C2×D13—42no—
123C2×D13—162no—
124C2×D13—161no—
125C2×D13C2×D812yes—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13C2×D811yescharacteristic
129C4×C13C22×D411yescharacteristic
130Dic13—41no—
131Dic13C2×D812yes—
1322−1+4—261no—
133H(5,𝔽2)—261no—
134#137—262no—
135#137—261no—
136AGL(1,ℤ/8)—262no—
137AGL(1,ℤ/8)—261no—
138#135—132no—
139#135—132no—
140#135—131no—
141#135C2×D1311yescharacteristic
142C2×Q16—132no—
143C2×Q16C2×D1311yescharacteristic, complemented
144C2×D8—132no—
145C2×D8—131no—
146#131—131no—
147Q32—131no—
148Q32C2×D1312yescomplemented
149SD32—132no—
150SD32—132no—
151SD32—131no—
152SD32—131no—
153SD32—132no—
154SD32C2×D1312yescomplemented
155D16—131no—
156D16—132no—
157M32—132no—
158M32C2×D1311yescharacteristic, complemented
159C2×C16—131no—
160C2×C16—132no—
161C2×C13—21no—
162C2×C13—81no—
163C2×C13C22×D811yescharacteristic
164D13—22no—
165D13—81no—
166D13—82no—
167#41—21no—
168#41—131no—
169#41—262no—
170#41—262no—
171#41—261no—
172#41—522no—
173#41—521no—
174#41—521no—
175C2×Q8—21no—
176C2×Q8—262no—
177C2×Q8—521no—
178C2×D4—262no—
179C2×D4—261no—
180C2×D4—521no—
181C2×D4—522no—
182Q16—21no—
183Q16—131no—
184Q16—262no—
185Q16C22×D1312yes—
186Q16C22×D1311yescharacteristic
187SD16—21no—
188SD16—262no—
189SD16—262no—
190SD16—261no—
191D8—131no—
192D8—132no—
193D8—262no—
194D8—261no—
195D8C22×D1311yescharacteristic
196M16—131no—
197M16—132no—
198C2×C8—132no—
199C2×C8C22×D1311yescharacteristic
200C16—131no—
201C16—131no—
202C16C22×D1312yes—
203C13#341611yescharacteristic, complemented, Sylow
204C23—522no—
205C23—521no—
206Q8—21no—
207Q8—22no—
208Q8—41no—
209Q8—131no—
210Q8—261no—
211Q8—522no—
212D4—21no—
213D4—41no—
214D4—132no—
215D4—131no—
216D4—262no—
217D4—261no—
218D4—522no—
219D4—522no—
220D4—522no—
221D4—521no—
222D4—521no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—132no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—521no—
230C2×C4D4×D1311yescharacteristic
231C8—132no—
232C8D4×D1311yescharacteristic
233C8C23×D1311yescharacteristic
234C22—41no—
235C22—132no—
236C22—521no—
237C22—522no—
238C22—2081no—
239C22—2082no—
240C22D8×D1311yescharacteristic
241C4—41no—
242C4—42no—
243C4—132no—
244C4—521no—
245C4D8×D1311yescharacteristic
246C4C2×D4×D1311yescharacteristic
247C2—21no—
248C2—81no—
249C2—262no—
250C2—1042no—
251C2—1041no—
252C2C2×D8×D1311yescharacteristic
subgroupG/H
centerC2C2×D8×D13
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC13×#510C2
socleC2×C13C22×D8
hypercenter#510D13
hypocenterC13#3416
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11719474C2semidirect
2. #11719471C2semidirect
3. C13×#510C2semidirect
4. #11718855C2semidirect
5. C2×#88068C2semidirect
6. #11718580C2semidirect
7. #11718579C2semidirect
8. #11718575C2semidirect
9. D13×SD32C2semidirect
10. #11718569C2semidirect
11. #11718568C2semidirect
15. C2×C13×Q16C22semidirect
19. #88173C22semidirect
21. Q16×D13C22semidirect
24. #88158C22semidirect
27. C13×Q32C22semidirect
28. C13×SD32C22semidirect
29. C13×M32C22semidirect
30. #88069C22semidirect
31. #88068C22semidirect
32. #88068C22semidirect
33. #88068C22semidirect
34. #88067C22semidirect
35. #88066C22semidirect
36. C2×#6090C22semidirect
37. #88040C22semidirect
38. D208C22semidirect
39. #88038C22semidirect
40. C16×D13C22semidirect
111. #510D13semidirect
143. C2×Q16C2×D13semidirect
148. Q32C2×D13semidirect
154. SD32C2×D13semidirect
158. M32C2×D13semidirect
203. C13#3416semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117194742
#117194712
C13×#5102
#117188552
C2×#880682
#117185802
#117185792
#117185752
D13×SD322
#117185692
#117185682
#341613